Path integral methods for reaction rates in complex systems.

We shall use this introduction to the Faraday Discussion on quantum effects in complex systems to review the recent progress that has been made in using imaginary time path integral methods to calculate chemical reaction rates. As a result of this progress, it is now routinely possible to calculate accurate rate constants including quantum mechanical zero point energy and tunnelling effects for arbitrarily complex (anharmonic and multi-dimensional) systems. This is true in the adiabatic (Born-Oppenheimer) limit, in the non-adiabatic (Fermi Golden Rule) limit, and everywhere between these two limits in the normal Marcus regime. Quantum mechanical effects on reaction rates can be enormous, even at room temperature, and the problem of including these effects in simulations of a wide variety of chemical reactions in complex systems has now effectively been solved.